Illuminance is the amount of light that falls onto a given area. For example, it is the amount of light that falls per square millimeter. Luminance is the amount of light that is emitted from a given area from a given angle. Luminance has a directional component to it. Luminance is most closely related to brightness and most closely related to what a person sees. Flux density is a measure of illuminance.
Radiometry is the measurement of radiant power at every wavelength across a wide portion of the electromagnetic spectrum. Radiometric measurements are often used to characterize the spectral power distribution of electric light sources. FIG. 1 is a graph with curves showing light source spectral power distributions. Curve 10 shows the spectral power distribution for incandescent lights. Curve 12 shows the spectral power distribution for typical fluorescent lights. Curve 14 shows the spectral power distribution for a white light emitting diode (LED). Radiometric measurements are rarely made outside sophisticated laboratories, however, because accurate radiometric instruments are expensive and impractical for field measurements. Consequently lighting standards and recommendations for offices, schools, factories, etc. are almost never specified in radiometric terms.
Photometry is the measurement of radiation within the visible region of the electromagnetic spectrum using a broadband spectral weighting function, usually the photopic luminous efficiency function (Vλ). The Vλfunction was established by the Commission Internationale de I'Eclairage (CIE) in 1924. It is based upon a number of studies of the spectral sensitivity of the human fovea performed in the 1920s. As subsequent research has shown, Vλ characterizes the spectral sensitivity of the two most prevalent cone photoreceptor types (L and M cones) in the fovea. In 1924, Vλ became part of the international definition of “light.”
The CIE also defined in 1951 a scotopic luminous efficiency function (V′λ) which represents the spectral sensitivity of rods in the peripheral retina. In 1964, the CIE also published, but did not officially approve, another photopic luminous efficiency function for cone photoreceptors in the peripheral retina out to 10 degrees (V10λ), which also has proven useful in characterizing the spectral sensitivity of the peripheral retina when cones dominate visual response. FIG. 2 shows these luminous efficiency functions. In FIG. 2, curve 20 illustrates a luminous efficiency function for photopic light in a two degree field; curve 18 illustrates a luminous efficiency function for photopic light in a 10 degree field; and curve 16 illustrates a luminous efficiency function for scotopic light.
In photometry, complete characterization of the spectral power distribution of the light source(s) is reduced to a single number, either illuminance lux or footcandle (lx or fc) or luminance candelas per square meter or footlamberts (cd m−2 or fL). When properly calibrated, photometric equipment can provide accurate values within about plus or minus 5% of either illuminance or luminance, depending upon the instrument. Accurate illuminance measurements can be obtained from instruments costing approximately $500 US, whereas similar accuracy for luminance measurements might require an investment of $2000 US because more sophisticated optics are required.
Lighting standards and lighting practices are almost exclusively dominated by illuminance specifications and measurements. Most likely, this reflects the practical and inexpensive nature of the illuminance meters used to measure compliance with the required specifications. Indeed, in the last century, illuminance specifications and measurements were the primary, if not the only, measure of lighting specification and compliance for both indoor and outdoor applications.
Research conducted over the past 50 years has repeatedly shown that Vλ is a fairly accurate representation of the spectral sensitivity of the human fovea for such tasks as reading alphanumeric text, threading needles, and visual acuity. This research is discussed in a paper entitled “Relationships between office task performance and ratings of feelings and task evaluations under different light sources and levels,” by S. W. Smith et al., published in Proc. Commission Internationale de I'Eclairage, 19th Sess., p. 207 (Kyoto, Japan: Commission Internationale de I'Eclairage) (1980), and in a book entitled “Human Factors in Lighting,” by P. R. Boyce, published by Applied Science Publishers (London 1981). Because most tasks performed in offices, factories, and schools require good foveal vision, photometric measurements based upon Vλ have been extremely useful in characterizing “light” for visual tasks in interior applications. More significantly perhaps, lighting practitioners have found illuminance measurements useful. It should be emphasized again that the lighting levels in every commercial and industrial building in North America are specified in terms of illuminance. This very high level of acceptance by lighting practitioners reflects the utility of illuminance in characterizing and communicating light levels for interior applications.
Lighting practitioners have not readily accepted illuminance measurements based upon Vλ, however, as a useful characterization of “light” for outdoor applications. For example, many practitioners have argued that high-pressure sodium (HPS), a yellowish-white lamp that is the dominant light source in outdoor applications, provides poorer visibility at the same illuminance than “whiter” sources like metal halide (MH) or fluorescent. Recent research shows that these observations are valid for some visual tasks but not for others. It seems that, for tasks dominated by foveal vision, illuminance, based on Vλ, remains a useful characterization of “light” at any light level. For off-axis visual tasks requiring movement detection, however, it is clear that Vλ does not characterize the spectral sensitivity of the peripheral retina at low light levels commonly used in outdoor applications. This issue is discussed in a paper entitled “Evaluating light source efficacy under mesopic conditions using reaction times,” by Y. He et al., published in J. Illum. Eng. Soc., Vol. 26, page 125 (1997); a paper entitled “A system of mesopic photometry,” published in Light. Res. Technol., by Y. He et al., Vol. 30, p. 175 (1998); and in a paper entitled “The road not taken,” by M. S. Rea, published in Lighting J., Vol. 66, page 18 (2001).
He et al. have recently developed a model of luminous efficiency based on reaction times to peripheral objects at low, so-called, mesopic levels (discussed below). The development of the model is contained in a paper entitled “Evaluating light source efficiency under mesopic conditions using reaction times,” by Y. He et al., published in J. Illum. Eng. Soc., Vol. 26, p. 125 (1997); and in a paper entitled “A system of mesopic photometry,” by Y. He et al., published in Light. Res. Technol., Vol. 30, p. 175 (1998). This model differs from brightness-based models in that it models responses mediated by the magnocellular visual channel, which is the same visual channel modeled by Vλ at higher luminances and in the fovea.
Brightness-based models are discussed in a paper entitled “Standard observer for large-field photometry at any level,” by D. A. Palmer, published in J. Opt. Soc. Am., Vol. 58, p. 1296 (1968); and in a paper entitled “System of mesopic photometry for evaluating lights in terms of comparative brightness relationships,” by K. Sagawa et al., published in J. Opt. Soc. Am., Vol. 9, p. 1240 (1992). The visual channel modeled by Vλ is discussed in a paper entitled “Luminance,” by P. Lennie et al., published in J. Opt. Soc. Am. A, Vol. 10, p. 1283 (1993). Brightness perception, mediated by the parvocellular visual channel, has been found to be distinctly nonadditive for light sources of different spectral power distributions. This is discussed in a report entitled “Mesopic Photometry: History, Special Problems and Practical Solutions” (Vienna: Commission Internationale de I'Eclairage) (1989).
The research by He et al. shows that the spectral sensitivity of the peripheral retina changes with light level over the range of mesopic adaptation conditions, shifting continuously from photopic (V10λ, which captures the response of the peripheral cones with a peak sensitivity at 555 nm) to scotopic (V′λ, capturing the rods' response with a peak sensitivity at 507 nm) sensitivity as light levels are reduced. Depending upon the visual task and the reflectance of the target and its background, the mesopic region corresponds to illuminance levels between approximately 30 and 0.02 lx. Actual nighttime illuminance levels produced by electric light sources are typically between 0.5 and 100 lx. This is shown in a book entitled “Lighting Handbook: Reference and Application,” 9th edition, M. Rea (ed.), published by the New York Illuminating Engineering Society of North America (2000 IESNA). Although basic research is useful-in providing scientists with a better understanding of the spectral sensitivity of the human retina at these light levels, research will have little impact on lighting standards or practices until a useful and inexpensive instrument for measuring flux density at mesopic light levels is developed.
A previous device has approximated the spatial efficiency of the eye to determine the total amount of light falling on the retina. This device was discussed in a paper entitled “Design and optimization of a retinal exposure detector,” by John Van Derlofske et al., published in SPIE Proc. 4092, p. 60 (2000) (hereinafter “the Van Derlofske paper”).
The spatial efficiency function of the eye has two components, the cutoff due to facial structure (brow, nose, and cheek) and the spatial efficiency of the eye itself. A standard cutoff function for facial structure has been published in “Engineering Data Compendium: Human Perception and Performance,” by K. R. Boff et al. (ed.), Dayton, Ohio: Armstrong Aerospace Medical Research Laboratory (1988). The spatial efficiency of the eye was determined through computer modeling as discussed in the Van Derlofske paper. A detailed eye model was created in optical modeling software, reproducing all of the important physical and optical properties of the eye. Physical surfaces and volumes modeled include the anterior cornea, the posterior cornea, the aqueous, the anterior lens, the posterior lens, the vitreous, and the retina. Standard optical modeling properties, such as refractive index, surface shape, and thickness, were applied to the model. In addition, other physiological and optical parameters were applied to ensure accuracy. These parameters were determined from the literature or dictated by the assumptions described below.
The pupil diameter was set to 5 mm, chosen as a median diameter. The human pupil ranges on average in diameter from approximately 2 mm, at high light level conditions, to approximately 8 mm at low light levels. The pupil is positioned directly in front of the lens but is not exactly centered with respect to the rest of the eye. It is decentered nasally by about 0.5 mm. Another assumption in eye physiology was made in the area where the muscle attaches to the lens. This area is critical in defining the vignetting or high angle cutoff of the eye. Here the lens edge/muscle tissue area was kept as small as possible while still remaining realistic. This approximation maximized the high angle limit of light acceptance into the eye while retaining physiological accuracy.
Relevant optical properties describing light loss mechanisms in the human eye were also included in the previous model to ensure accuracy. These include the application of Fresnel reflection/transmission and volume attenuation in the eye media. Fresnel reflection/transmission at each surface was used to account for energy loss due to partial reflection. An average volume attenuation value of α=0.1238 mm−1 (at 555 nm) was used to account for scattering and absorption in the lens as a function of the path length of the incident light. The lens optical densities from which this value was calculated were reported as being from young eyes, although some of those data were from subjects of age up to 45 years. After an age of approximately 30 years, the attenuation coefficient a will increase, but the rate of this increase is greatest for wavelengths shorter than 500 nm due to increased yellowing of the lens. For wavelengths longer than 500 nm, the increased rate of attenuation is much lower, so the value of α is representative for young to middle-aged adults.
The total theoretical spatial efficiency function is shown in FIG. 3 as temporal and brow cross sections on a linear angular scale. Curve 22 illustrates the cross section of the temple to nose and curve 24 illustrates the cross section of the brow to cheek. A linear scale is used so the fine structure and differences in the distributions can be easily seen and compared. The x-axis represents the source angle relative to the eye's optical axis and the y-axis represents the relative amount of flux incident on the retina.
The response curves differ slightly from a cosine distribution. They start slightly narrower than a cosine function at small angles and become slightly wider than a cosine at large angles. The shape of this function is largely dictated by the apparent size of the pupil and by the path length of the light traveling through the ocular media. The sharp cutoff at high angles is mostly due to vignetting or light blocking by the facial structure. Only in the temporal direction, where the facial structure is not a factor, does vignetting in the eye itself become important. Within the eye, vignetting is due to light blocking by the edge of the iris and the lens. The distribution is also slightly shifted in the x dimension due to the nasal shift of the pupil. These differences amount to a discrepancy of up to 6% in the total integrated response for uniform luminance viewing fields compared to a cosine response.
The parameters that were used to model the eye in order to prepare the previous device are shown in FIG. 4. In FIG. 4, the features identified in column 45 are various parts of the eye: row 30 is the anterior cornea; row 32 is the posterior cornea; row 34 is the aqueous; row 36 is the anterior lens; and row 38 is the mid lens. The designation of a mid lens is an imaginary surface that divides the two gradient index regions. Row 40 is the posterior lens; row 42 is the vitreous; and row 44 is the retina.
The columns from column 46 to column 52 identify the parameters used for each feature of the eye. Column 46 is the radius in millimeters; column 48 is the asphericity Q, defined below; and column 50 is the thickness in millimeters of each feature. This thickness is the distance from the identified feature to the surface of the next feature. For example, it is 0.50 mm from the anterior cornea to the surface of the posterior cornea. Column 52 is the refractive index n of each feature of the eye assuming that light at 555 nm is received by the eye.
More specifically, the asphericity Q describes the conic shape of the surface and is defined by,y2+(1+Q)z2−2zR=0,  (1)where z is the distance along the optic axis, y is the perpendicular distance from optic axis, and R is the radius. Grad A (column 52, row 36) and Grad P (column 52, row 40) refer to gradient or nonhomogeneous refractive indices. The index of refraction describes how light refracts, reflects, and propagates in a medium. A gradient index is one that is variable with position in the media. In this case it is given by the equationn(w,z)=n00+n01z+n02z2+n10w2,  (2)where z is again the distance along the optical axis and w is the radial distance perpendicular to the optical axis, orw2=x2+y2.  (3)For Grad A: n00=1.368, n01=0.049057, n02=−0.015427, and n10=−0.001978. For Grad P: n00=1.407, n01=0.00000, n02=−0.006605, and n10=−0.001978.
Using the above parameters, an optically and anatomically correct computer model of the human eye was developed in both LightTools® (by Optical Research Associates) and ASAP® (by Breault Research Organization) optical modeling software. Light rays were traced in these models and the retinal illuminance results were used to determine the spatial response function. The more complete ASAP® model includes optical properties such as gradient refractive index and volume attenuation that were not definable in the LightTools® model. FIG. 5 shows a sagital section of the optical axis of the 3D ASAP® model of an eye 60 including the anterior cornea 62, the posterior cornea 64, the aqueous 66, the anterior lens 68, the mid lens 70, the posterior lens 72, the visreous 74, and the retina 76.
Using the parameters defined in FIG. 4, standard optical modeling properties, such as refractive index, surface shape, and thickness, were applied to the model. In addition, other physiological and optical parameters were applied to the ASAP® model to ensure accuracy. These parameters were determined from the literature or dictated by assumptions made.
Relevant optical properties describing light loss mechanisms in the human eye were also included in the model to ensure accuracy. These include the application of Fresnel reflection/transmission and volume attenuation in the eye media. Fresnel reflection/transmission at each surface was used to account for energy loss due to partial reflection. An average volume attenuation value of α=0.1238 mm−1 (at 555 nm) was used to account for scattering and absorption in the lens and vitreous media as a function of the path length of the incident light.
Once the model was accurately entered into the software and all of the above parameters and properties were assigned, light rays were traced through the systems, using a monochromatic point source with a wavelength of 555 nm. The resulting spatial response function for the eye is shown in FIG. 6 in the x and y planes. More specifically, FIG. 6 illustrates the retinal response as a function of source angle in which curve 78 is the response in the x-plane and curve 80 is the response in the y-plane.
In FIG. 6, the x axis represents the source angle relative to the optical axis and the y axis represents the relative amount of flux incident on the retina. The plotted response curves differ from a cosine distribution. They start slightly narrower than a cosine function at small angles and become slightly wider than a cosine at large angles. The shape of this function is largely dictated by the apparent size of the pupil and by the path length of the light traveling through the ocular media. The sharp cutoff at high angles is due to vignetting or light blocking by the edge of the iris and lens. The distribution is also slightly shifted in the x dimension due to the nasal shift of the pupil.
With the eye's response function calculated from computer simulation and compared to other studies the total eye response function was determined by adding the facial cutoff. A standard facial cutoff function, as described below, was applied in three dimensions to the theoretically calculated retinal response function. The final results of the total retinal response function are shown by x-y slices in FIG. 7, which shows the data in FIG. 3 and links the x direction as the temple-to-nose direction and the y direction as the brow-to-cheek direction. More specifically, FIG. 7 is the retinal response as a function of source angle with facial structure. Curve 82 is the response in the x direction and curve 84 is the response in the y direction.
The computer modeling revealed that the spatial response of the human eye can be roughly approximated as a symmetrical cosine distribution with a highly asymmetrical and presumably sharp cutoff as affected by facial shading. The approach to designing the prior art retinal exposure detector followed the approach used in the computer modeling task by separating the response into that of the eye alone and that due to the effect of the facial shielding. Designing the prior art retinal exposure detector was performed in two steps: (1) designing the facial shading baffle, and (2) designing a detector assembly with a spatial response closely matching that given by the computer model of the eye.
FIG. 8 is a plot of the cutoff angle due to facial shielding based on data contained in a discussion entitled “Optics of the Eye,” in Engineering Data Compendium: Human Perception and performance, K. R. Boff et al. (eds.), Section 1.2 (Dayton Ohio: Armstrong Aerospace Medical Research Laboratory (1988) (hereinafter “the Boff reference”). Curve 86 is based on the eye data in the Boff reference. Curve 88 represents the configuration of the baffle used for the previous device. The shape of the baffle needed to produce the appropriate cutoff is made by cutting a sheet of flat material to the shape given by the plot of FIG. 8 and bending it around the cylindrical detector housing. The length, x, and height, y, of the flattened baffle is given by
                              x          =                      r            ·            θ                          ,                  y          =                      r                          tan              ⁡                              (                                                      ϕ                    c                                    ⁡                                      (                    θ                    )                                                  )                                                    ,                            (        4        )            where r is the radius of the detector housing, θ is the azimuth angle measured in the direction from cheek to temporal to brow to nose, and φc(θ) is the cutoff angle. The above equation was derived for a detector located at the center of the detector housing and having no spatial extent, i.e., a point receiver. The above equation specifies the baffle size where the detector is approximately half shaded.
FIG. 8 shows the measured cutoff angle (sensitivity less than 5% of maximum sensitivity) plotted with the desired cutoff angle from the Boff reference. The greatest deviation occurs at the temporal location where the actual cutoff of the eye extends past 90 degrees, yet the retinal exposure detector stops at 90 degrees due to the detector housing itself blocking the light at these large angles. This angular region is relatively unimportant to the total input light, however, because the eye accepts less than 5% of the light at these high angles as shown in FIG. 6.
FIG. 9 lists the component parameters for the previous device. Column 90 and rows 92 to 102 identify the features of the previous device: front lens, rear lens, front spacer, rear spacer, aperture, and diffuser. Columns 104 to 110 identify the parameters for the features identified in each row. Column 104 identifies the radius of curvature; column 106, the thickness, column 108, the diameter; and column 110, the refractive index n at 555 nm. The thickness shown in column 106 is the distance to the next surface. For example, in row 92, 12.0 mm is the distance from the front lens to the next surface of the rear lens. Accordingly, row 92 shows that the front lens has a radius of curvature of 11.46 mm, a thickness of 3.9 mm, a diameter of 12.0 mm, and a refractive index n of 1.457. Rows 94, 96, 98, 100, and 102 show that the radius of curvature of the rear lens, front spacer, rear spacer, aperture, and diffuser are all infinite. That is, they are substantially straight and without any curvature.
Row 94 also shows that the thickness of the rear lens is modeled as 0.0 mm, its diameter is 12.0 mm, and its refractive index is 1.457. Row 96 shows that the thickness of the front spacer is 1.0 mm, its diameter is 5.0 mm, and its refractive index is 1.56. Row 98 shows that the thickness of the rear spacer is 0.0 mm, its diameter is 5.0 mm, and its refractive index is 1.56. Row 100 shows that the thickness of the aperture is modeled as 0.0 mm, its diameter is 5.0 mm, and it has no refractive index. Row 102 shows that the diffuser has a thickness of 0.3 mm, a diameter of 12.5 mm, and a refractive index of 1.56.
The space between the front lens and the diffuser-aperture was filled with optical epoxy so that light would be transmitted from the lens to the diffuser. The purpose of having a space between the lens and the aperture-diffuser is to limit the large angle sensitivity of the detector assembly. A shorter space widens the spatial sensitivity while a longer space narrows the spatial sensitivity. Rays that strike the sides of the spacer are the large angle peripheral rays. Therefore, conduction of these rays to the diffuser increases the sensitivity of the detector assembly for large angles.
FIG. 10 is a cross-sectional view of an existing detector assembly and facial shield. Referring to FIG. 10, tube 138 serves as a housing for the detector. Inside tube 138 is a photocell 130, a photopic filter 128, and a diffuser 126. Two openings 142 and 144 are at the other end of the tube to hold a spacer 124 and a lens 122. Opening 142 defines the aperture of the device and acts like the iris of an eye. Opening 142 allows light to enter the inside of tube 138. Opening 142 has a diameter of 5.0 mm as shown in row 100 of FIG. 9. The characteristics of lens 122 are shown in rows 92 and 94 of FIG. 9. The characteristics of spacer 124 are shown in rows 96 and 98 of FIG. 9. The characteristics of opening 142 and diffuser 126 are shown in rows 100 and 102, respectively, of FIG. 9. The existing assembly also has a facial shield 120 designed as discussed above.
Although not often used by the lighting industry, the CIE established another luminous efficiency function, V′(λ), for scotopic, or very low, light levels in 1951. This function applies to large fields (central 20 degrees). In 1964, the CIE produced a provisional photopic function for the central 10 degrees, V10(λ), which, again, was not used by the lighting industry. Between photopic and scotopic conditions, spectral sensitivity shifts with light level. No official set of luminous efficiency functions has been established for intermediate, mesopic light levels.
Traditionally, mesopic vision has been assumed to cover the range from 0.001 to 3 cd m−2. There are many outdoor applications where light levels fall within this range, such as roadway, parking lot, and security lighting applications. Because there is no official mesopic photometry system recommended by the CIE, only photometers with a V(λ) luminous efficiency function are used to measure light at mesopic levels. This practice may produce measured light values with little relationship to the visual effectiveness of the light. Many attempts have been made to measure mesopic luminous efficiency functions and to develop a system of mesopic photometry.
A linear combination model (Equation 5) was proposed by He et al. in a paper entitled “Evaluating light source efficacies under mesopic conditions using reaction times,” published in J. Illum. Eng. Soc. 26(1), p. 125-138 (1997) (He I), and in a paper entitled “A system of mesopic photometry,” published in Lighting Res. Technol. 30(4), pp. 175-181 (1998) (He II):Vmes(λ,T10)=k(T10){x(T10)V10(λ)+[1−x(T10)]V(λ)},  (5)where Vmes represents the mesopic luminous efficiency as a function of wavelength, λ, and retinal illuminance, T10; V10 is the y10 function of the CIE 1964 supplementary (10 degrees field) standard observer, which is currently considered the most representative luminous efficiency function for large visual fields at photopic levels and is used here to calculate retinal illuminance, T10; V′(λ) is the CIE 1951 scotopic luminous efficiency function; x is the adaptation coefficient, which depends upon the photopic retinal illuminance of the reference light and varies between 0 and 1; and k is a normalization constant.
The relationship between the adaptation coefficient x and retinal illuminance is described by the following function using a least-squares solution in He II:x(T10)=0.0477T10+0.004  (6)
He II developed the following algorithm. The lower limit for the photopic vision can be estimated from Equation 6 by equating x to 1 and calculating the value of T10.
The value of x in Equation 6 is defined in terms of the photopic retinal illuminance of the reference light (589 nm in the He II experiment). Adaptation under mesopic conditions cannot be characterized by photopic trolands alone but should be determined by the excitation of rods and cones and, implicitly, lateral inhibition of rods by cones. Although the physiology of this interaction is not entirely clear, it must be true that the adaptation coefficient, x, is dependent on the adaptation spectrum as well as flux density on the retina. Ideally, Equation 6 should be defined in terms of mesopic trolands, Tmes, which would characterize the true mesopic adaptation level and therefore would be independent of a particular reference source.
A function relating x(Tmes) to Tmes can be determined using a least-squares method. This function is described by Equation 7:x(Tmes)=0.115(Tmes+0.006)0.71 for Tmes<21x(Tmes)=1 for Tmes≧21  (7)Equation 7 can be generally applied to any adapting spectrum and light level. The following computational procedure illustrates the approach disclosed in He II by which mesopic light level can be evaluated for any light source spectra.    (a) Measure the photopic luminance L (in cd m−2) for the spectral radiance distribution Le(λ) (in W m−2sr−1).    (b) Calculate the pupil size A (in mm2) of an average observer under L using the following equation adapted from a paper entitled “Luminance level conversions to assist lighting engineers use fundamental visual data,” by P. Trezona, published in Lighting Res. Technol. 15(2), p. 83-88 (1983):A=[5−3 tan h(0.41 log(L))]2/4  (8)     or from a paper entitled “Relative visual performance: A basis for application,” by M. S. Rea et al., published in Lighting Res. Technol. 23(3), p. 135-144 (1991):A=[4.77−2.44 tan h(0.31 log(L))]2/4  (8′)    (c) Calculate the retinal illuminance T10 (in photopic Td) and use T10 as an initial value for Tmes:T10=AKLe(λ)V10(λ)dλ  (9)     where K=683 lm W−1.    (d) Calculate the value of x(Tmes) using Equation 7.    (e) Use the value of x(Tmes) in Equation 10 to determine a mesopic luminous efficiency function Vmes(λ,Tmes):Vmes(λ,Tmes)=[x(Tmes)V10(λ)+(1−x(Tmes))V(λ)]  (10)    (f) Calculate the retinal illuminance Tmes (in mesopic T):Tmes=AKmesLe(λ)Vmes(λ,Tmes)dλ  (11)     where Kmes is a scaling factor equal to 683/Vmes(λ=555 nm) lm W−1.    (g) Use the resulting value of Tmes in Equation 7 and repeat the steps in Equations 8 through 11 until changes in Tmes are negligible.    (h) Calculate the mesopic luminance Lmes:Lmes=Tmes/A  (12)
To overcome the shortcomings of the existing detector, a new retinal flux density meter is provided. An object of the present invention is to make an optical system that mimics or approximates the light-collecting abilities of the eye. A related object is to create a meter that approximates the amount of light that enters into an eye, rather than approximating only the light that falls onto the plane of an eye. Another object is to provide a meter that measures the photopic and scotopic spectral responses of light incident upon the meter. It is still another object of the present invention to provide a method of approximating mesopic illuminance or flux density on the eye.